Seventeen subjects (nine women and eight men) from an outpatient, hospital-based treatment program for obesity volunteered. Within 10 days after the baseline measures (i.e., pretest measures) were obtained, the subjects began the 12-week VLCD [very low calorie diet] portion of the... program.... At the end of the 12 weeks, all measurements were repeated in the laboratory.

Figure 1 demonstrates the relationship between age and percent of weight loss as fat. The

correlation coefficient for this relationship was r = -.49. Correlation between hydrostatic weighing and bioelectrical impedance was r = .63 for the 16 pretests and r = .84 for the 17 posttests. (Hydrostatic measurement of one male subject was not pos- sible on the pretest because of discomfort in the water.) Correlation for the combined pretest and posttest trials (n = 33) was r - .837 (Figure 2).

1. Which figure illustrates a direct relationship? Explain.

2. Which figure has a negative slope? Is the corresponding correlation coefficient also negative?

3. If the line in Figure 1 was extended to the left, at what value would it meet the vertical axis (i.e., y-axis)? (Give an answer that is precise to one decimal place.)

4. What is the value of the intercept in Figure 2?

5. Is the relationship depicted in Figure 1 or in Figure 2 stronger? Explain.

6. Use the equation for the straight line shown in Figure 1to predict the percentage ofweight lost as fat for a person who is 60 years of age.

7. Use the equation for the straight line shown in Figure 1 to predict the percentage of weight lost as fat for a person who is 20 years of age.

8 . Compare your answers to Questions 6 and 7. Do your answers make sense considering that the relationship is inverse? Explain.

9. Use the equation for the straight line shown in Figure 2 to predict the percentage of body fat as measured by BIA for a person who has 50% body fat as measured by hydrodensitometry.

10. The equation in which figure will yield more accurate predictions? Explain.

11. Suppose the slope in Figure 2 had been 1.50 instead of 0.77. With a slope of 1.50, would the line rise (from left to right) more steeply or less steeply than the line shown in Figure 2?

12. The correlation coefficient for the relationship between the two methods for measuring body fat is less than perfect. What does this tell us about the two methods of measurement?

13. Speculate on why we use a line based on the entire group to make predictions instead of using the values of individuals to make predictions. (For instance, the person who is about 58 years of age in Figure 1 lost about 62% of weight as body fat. In the future, can we just predict that all in- dividuals who are 58 years of age will lose 62% body fat?)